Logic Puzzle: Truth Tellers
This is a classic logic puzzle where you must determine who is telling the truth based on everyone's statements.
Let's examine the statements:
- Pam: "I always tell the truth."
- Quentin: "Pam is lying."
- Roger: "Both Pam and Quentin are lying."
- Terry: "Everyone is telling the truth."
- Susan: "Everyone is lying."
Now, let's analyze each statement:
If Pam is telling the truth about always telling the truth, then Quentin must also be telling the truth when he says "Pam is lying," which would be a contradiction.
If Quentin's statement that "Pam is lying" is true, then Pam's claim to always tell the truth is false.
If Roger is telling the truth about "Both Pam and Quentin are lying," it would make his statement true and Pam's and Quentin's false.
Terry's statement that "Everyone is telling the truth" cannot be true because that would conflict with Quentin's statement that "Pam is lying." If everyone were telling the truth, then Quentin's statement would mean Pam is indeed lying, which makes her statement false and contradicts Terry's statement.
Susan's statement that "Everyone is lying" also cannot be true, because if it were, then her statement would be true, which means not everyone is lying.
The only scenario which does not result in a contradiction is if Roger is the only one telling the truth, with the following conditions:
- Pam is lying about always telling the truth.
- Quentin is lying because Pam is not always telling the truth.
- Terry is lying because it's evident that not everyone is telling the truth.
- Susan is lying because if everyone were lying, her statement would be lying about everyone lying, but her own lie would make her statement partially true, thus not everyone is lying.
Therefore, Roger is the only one telling the truth, which means the answer is:
B) 1
